## The median- graphical method -progression , Mathematics

Assignment Help:

The median

- it is a statistical value which is usually located at the center of a given set of data that has been organized in the order of size or magnitude as illustrating, consider the set 14, 17, 9, 8, 20, 32, 18, 14.5, 13. While the data is ordered it will be 8, 9, 13, 14, 14.5, 17, 18, 20, 32

The middle number or median is 14.5

-  The significance of the median lies in the fact that it divides the data into two equivalent halves. The number of observations above and below the median is equal.

-   In order to find out the value of the median from grouped data. While data is grouped the median may be determined by utilizing the given methods.

i.  Graphical method by using the cumulative frequency curve or ogive

ii.  The formula

Illustration

Referring to the table which is given below; determine the median by using the methods above

 IQ No of resid UCB Cumulative Frequency 0 - 20 6 20 6 20 - 40 18 40 24 40 - 60 32 60 56 60 - 80 48 80 104 80 - 100 27 100 131 100 - 120 13 120 144 120 - 140 2 140 146 Hence the position of the median is= (n + 1)/2

= (146 + 1)/2

ii. Computation

The formula utilized is Whereas L = Lower class boundary of the class having the median

N = No of observations

Cfo= cfbm = Cumulative frequency of the class before that having the median

F1 fmc = Frequency of the class having the median = 60 + ((73.5 - 56)/48) * 20

= 60 + 7.29

= 67.29

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